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Simplifying w2 + 22w = 43 Reorder the terms: 22w + w2 = 43 Solving 22w + w2 = 43 Solving for variable 'w'. Reorder the terms: -43 + 22w + w2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + 22w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + 22w + 43 + w2 = 0 + 43 Reorder the terms: -43 + 43 + 22w + w2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 22w + w2 = 0 + 43 22w + w2 = 0 + 43 Combine like terms: 0 + 43 = 43 22w + w2 = 43 The w term is 22w. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22w + 121 + w2 = 43 + 121 Reorder the terms: 121 + 22w + w2 = 43 + 121 Combine like terms: 43 + 121 = 164 121 + 22w + w2 = 164 Factor a perfect square on the left side: (w + 11)(w + 11) = 164 Calculate the square root of the right side: 12.806248475 Break this problem into two subproblems by setting (w + 11) equal to 12.806248475 and -12.806248475.Subproblem 1
w + 11 = 12.806248475 Simplifying w + 11 = 12.806248475 Reorder the terms: 11 + w = 12.806248475 Solving 11 + w = 12.806248475 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + w = 12.806248475 + -11 Combine like terms: 11 + -11 = 0 0 + w = 12.806248475 + -11 w = 12.806248475 + -11 Combine like terms: 12.806248475 + -11 = 1.806248475 w = 1.806248475 Simplifying w = 1.806248475Subproblem 2
w + 11 = -12.806248475 Simplifying w + 11 = -12.806248475 Reorder the terms: 11 + w = -12.806248475 Solving 11 + w = -12.806248475 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + w = -12.806248475 + -11 Combine like terms: 11 + -11 = 0 0 + w = -12.806248475 + -11 w = -12.806248475 + -11 Combine like terms: -12.806248475 + -11 = -23.806248475 w = -23.806248475 Simplifying w = -23.806248475Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.806248475, -23.806248475}
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